Introduction

Abstract

In a short example we want to illustrate some of the concepts this book is about. Let us consider the two dimensional Poisson problem as a homogeneous Dirichlet boundary value problem

$$\begin{array}{l} - \Delta u\, = \,f\,in\,\Omega ,\\ u\, = \,0\,on\,\partial \Omega , \end{array}$$

(1.1)

where Δu = ∂²u/∂x² + ∂²u/∂y² is the Laplace operator, Ω is a bounded, open domain like [0, 1]² whose boundary is dentoed by ∂Ω.